Variable cross-coupling partial reflector and method

ABSTRACT

When illuminated with a plane wave a variable cross-coupling partial reflector reflects a specific amount of a cross-polarized field and a specific amount of a co-polarized field and transmits the remaining power with low attenuation. This is achieved with a pair of frequency selective surfaces (FSS) that are rotated with respect to the incident plane wave. The FSSs can be fixed with a given alignment for a particular application or a tuning mechanism can be provided to independently rotate the surfaces and adapt the reflected co- and cross-polarized fields to changing requirements. Of particular interest is the ability to provide a specific amount of cross-polarized reflected power while reflecting no co-polarized field over a certain range of wavelengths. This will be useful to increase power efficiency in, for example, wave power sources that utilize quasi-optical power by causing oscillations in reflection amplifier arrays.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a partial cross-coupling reflector for use inquasi-optical millimeter wave power sources, and more specifically to avariable reflector that can select the amount of reflected power in boththe co-polarized (co-pol) and cross-polarized (x-pol) fields.

2. Description of the Related Art

Power is difficult to produce at millimeter wave frequencies due to thelower power output of transistors and the losses incurred by traditionalpower combiners at these frequencies. Free space combining, also called“quasi optical” combining, eliminates the latter problem by allowingelectromagnetic energy to combine in free space. Quasi optical arrayscan provide high power by combining the outputs of many (e.g. thousands)of elements.

Quasi optical amplifiers arranged in arrays have been developed by anumber of groups to produce high output powers at millimeter wavefrequencies. These amplifier arrays amplify incoming radiation, eitherthrough reflection or transmission, and reradiate energy typically in a(more or less) gaussian mode. The amplifiers ususally utilize crossedinput and output polarizations in order to reduce input/output couplingand avoid oscillation.

Quasi optical sources (oscillators) arranged in arrays have also beendeveloped for millimeter wave power, and consist of a number ofindividual oscillators that are coupled together so that they mutuallysynchronize in phase and the radiation from all the elements combinescoherently, typically in a (more or less) gaussian mode in front of theoscillator array. A number of different methods exist to realize thecoupling network, from printed circuit transmission lines to partialreflectors. The key is to provide strong coupling between elements toensure in-phase oscillation.

Many quasi optical oscillator arrays utilize hardwire circuitry (e.g.printed circuits, waveguides) to couple together the oscillatingelements. For these types of arrays it is very difficult to control ormodify the coupling in real time, without resorting to complicatedschemes that are difficult to realize. For quasi optical arrays thatutilize cavity resonators, the oscillators are usually one port devices(negative resistance oscillators) with a single polarization output,which increases parasitic mutual coupling, creating difficulty incontrolling the coupling between elements.

A cavity resonator is typically realized using a total reflector and apartial reflector spaced a distance apart. Multiple reflections betweenthe two reflectors creates standing waves at discrete resonantfrequencies. The purpose of the partial reflector is to allow usefulpower to flow out of the structure. A typical partial reflector consistsof a single grating. If the grating is is aligned with the polarizationof an incident plane wave, the co-pol field will be reflected. Byrotating the grating, specific amounts of the co-pol or x-pol field canbe reflected. However, the other component of the reflected field is notcontrolled. In typical wave sources, one wants to control either the co-or x-pol component while nulling the other component to zero. Thereforethe uncontrolled component is dissipated as energy, which makes thesource less efficient.

SUMMARY OF THE INVENTION

The present invention provides a partial cross-coupling reflector foruse in quasi-optical millimeter wave power sources or other systems thatutilize “quasi optical” combining that can select the amount ofreflected power in both the co- and x-pol fields.

This is accomplished with a first frequency selective surface (FSS)(e.g. grating) rotated by a first angle φ₁ with respect to thepolarization of an incident plane wave and a second FSS spaced behindthe first FSS and rotated by a second angle φ_(d) with respect to thefirst FSS. The angles φ₁, φ_(d) are selected so that the magnitude ofthe net reflection of the incident plane wave from the cross-couplingreflector has approximately a specific amount (Γ_(x-pol)) of across-polarized field of the plane wave and approximately a specificamount (Γ_(co-pol)) of a co-polarized field of the plane wave for aspecified bandwidth. In one embodiment, the FSSs are fixed at thespecified angles. In another embodiment, a tuning mechanism is providedfor rotating the first and second FSSs with respect to the polarizationof an incident plane wave to the first and second angles. The reflectormay be provided with a look-up table of angles (φ₁, φ_(d)) for specified(Γ_(x-pol), Γ_(co-pol)).

These and other features and advantages of the invention will beapparent to those skilled in the art from the following detaileddescription of preferred embodiments, taken together with theaccompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a variable cross-coupling partial reflector inaccordance with the present invention;

FIG. 2 is a plot of the possible values of Γ_(x-pol), Γ_(co-pol) thatcan be realized with the variable cross-coupling partial reflector,assuming a λ/2 tine thickness and λ/4 grating spacing;

FIG. 3 is a four-port network equivalent circuit for the partialreflector;

FIGS. 4 a-4 c are a sequence of grating diagrams illustrating thephysical operation of the partial reflector;

FIG. 5 is a flow diagram of an embodiment for characterizing the partialreflector and storing the (φ₁, φ_(d)) pairs for specified (Γ_(x-pol),Γ_(co-pol)) pairs in a look-up table (LUT);

FIG. 6 is a section view of an embodiment of the partial reflector inwhich a series of metal bars of rectangular cross section are cutthrough a plate;

FIGS. 7 a-7 c are plots of the co- and cross-pol reflective fieldmagnitudes normalized to the incident field magnitude in which thedesired cross-pol varies from −5 to −15 dB and the desired co-pol is setto zero for a given bandwidth;

FIG. 8 is a diagram of a partial reflector including a pair of planardielectric gratings formed on respective circuit boards and a tuningmechanism for rotating each grating;

FIG. 9 is a section view a quasi-optical amplifier/oscillator arrayusing the variable cross-coupling partial reflector; and

FIG. 10 is a diagram of one element of the quasi-opticalamplifier/oscillator array.

DETAILED DESCRIPTION OF THE INVENTION

The present invention describes a variable cross-coupling partialreflector when illuminated with a plane wave reflects a specific amountof a x-pol field and a specific amount of a co-pol field and transmitsthe remaining power with low attenuation. This is achieved with a pairof frequency selective surfaces (FSS) that are rotated with respect tothe incident plane wave. The FSSs can be fixed with a given alignmentfor a particular application or a tuning mechanism can be provided toindependently rotate the surfaces and adapt the reflected co- andcross-polarized fields to changing requirements. Of particular interestis the ability to provide a specific amount of x-pol reflected powerwhile reflecting no co-pol field over a certain range of wavelengths orvice-versa. This will be useful to increase power efficiency in, forexample, wave power sources that utilize quasi-optical power by causingoscillations in reflection amplifier arrays.

A Frequency Selective Surface (FSS) is any surface that scatterspolarized plane waves in specific ways. Some FSSs act as filters thatpass frequencies within some bandwidth and reflect other frequencies.The FSSs of interest to the present application ideally provide 100%reflection to linearly polarized plane waves of one polarization andprovide 100% transmission to the orthogonally polarized waves. Theembodiments of the invention will be described for a grating but ameandering circuit trace could also be configured as a FSS. Furthermorethe embodiments of the invention will be described for the typical caseof normally-incident linearly-polarized plane waves. However, thepartial reflector could be configured for use with obliquely incidentplane waves and/or arbitrarily polarized plane waves, which wouldrequire some changes to the physical design of the gratings, spacing ofthe gratings and the characteristic equations given below for thepartial reflector. Such modifications would be well understood by thoseof ordinary skill in the art.

As illustrated in FIG. 1, a variable cross-coupling partial reflector 10consists of a pair of polarization gratings 12 and 14. Reflector 10 isilluminated with a linearly polarized plane wave 16 and reflects aco-pol field 18 and x-pol field 20 and transmits co- and cross-polarizedfields 21 and 22, respectively. The co-pol and x-pol are defined withrespect to the incident polarization. Each of the gratings substantiallyreflects waves that have a polarization that lies along the grating andsubstantially transmits waves that are polarized orthogonally to thegrating. By orienting the two gratings properly at angles φ₁ withrespect to the incident polarization and φ_(d) with respect to φ₁, onecan achieve specific amounts (Γ_(co-pol), Γ_(x-pol)) of co- and x-polreflection in fields 18 and 20 normalized to the incident plane wavemagnitude. The remaining energy is transmitted through the device infields 21 and 22 with a small amount of attenuation in the reflector.

To implement the partial reflector, one must design a suitable grating.The parameters of the grating include tine width, tine spacing, gratingthickness d and grating diameter D. Typically, the center-to-center tinespacing is chosen to be less than one wavelength λ0 at the highestfrequency of operation, typically ˜0.5 λ. The tine width is typically˜0.5 the tine spacing. Smaller is better, but more difficult tofabricate. The grating thickness d is the most sensitive parameter andis chosen ˜0.5 λ so that reflection from the front and back surfaces ofthe grating cancel one another. To choose the thickness, the grating issimulated using an EM solver and the thickness is selected to cancel thereflected fields for an incident polarization that is orthogonal to thedirection of the grating tines. The polarization gratings are designedwith a diameter D that is large enough for the application of interest.In practice, D will typically range from a few wavelengths to manyhundreds of wavelengths.

The spacing ‘s’ of the gratings is also an important parameter. An s˜¼ λspacing (or odd multiples thereof) is optimal to maximize the range ofreflection coefficients over which the co-pol and x-pol fields can betuned and is less sensitive to errors in spacing. The spacing maydeviate from the optimum and still function adequately but the spacingcan not (ideally) be a multiple of ½ λ. Assuming ideal gratings, at ½ λmultiple reflections between the gratings produce 100% co-pol reflectionof the incident plane wave, independent of the grating angles.

Assuming ideal gratings and a normally incident linearly polarized planewave, the relationship between (φ₁, φ_(d)) and (Γ_(x-pol), Γ_(co-pol))is given by:

$\begin{matrix}{{\phi_{1} = {\cot^{- 1}\left( \frac{\Gamma_{x - {pol}}}{1 + \Gamma_{{co} - {pol}}} \right)}},{and}} & (1) \\{\phi_{d} = {{\cos^{- 1}\left( \sqrt{\frac{{\cos\left( {2\left( {\phi_{1} - \frac{\pi}{2}} \right)} \right)} - \Gamma_{{co} - {pol}}}{1 + \Gamma_{{co} - {pol}}}} \right)}.}} & (2)\end{matrix}$Equations (1) and (2) will provide angles (φ₁, φ_(d)) that for welldesigned and properly constructed gratings and a substantially normalplane wave will produce actual reflected cross-polarized andco-polarized fields within a “reasonable approximation” of the idealvalues, e.g. no worse than a 3 dB deviation. The gamma values are oftenexpressed in dB but should be in numeric form when entered into theequations. Γ_(numeric)=exp(Γ_(d/B)/2).

The angles φ₁, φ_(d) can be selected to achieve any desired amounts|Γ_(x-pol|), |Γ_(co-pol)| of the x-pol and co-pol field magnitudes.Using the described approach, the phases of the co- and x-pol fields arealways equal to the incident field (with a possible phase reversal).Thus, the possible values of Γ_(x-pol), Γ_(co-pol) that can be realizedusing this invention can be plotted on a 2D graph 23 as shown in FIG. 2.The outer perimeter 24 a is bounded by the circle|Γ_(co-pol)|²+|Γ_(x-pol)|²<1, which is the result of power conservation.The inner perimeter 24 b is bounded by the circle|Γ_(co-pol)+0.5|²+|Γ_(x-pol)|²>0.25. This is a result of the constraintsthat were imposed on the structure, namely gratings that eitherperfectly reflector or perfectly transmit, quarter wave spacing, halfwavelength tines, etc. This limitation does not pose any problems inpractice since most applications are concerned only with reflectedmagnitudes of components and not phase values. The area between theinner and outer inner perimeters defines the set of allowable solutions25 as indicated by the shaded area in FIG. 2.

The cases in which the co-pol reflected component is nulled are ofparticular interest in quasi-optical wave sources.

Case 1: Γ_(co-pol)=0

In this case the first grating is rotated by φ₁=cot⁻¹(Γ_(x-pol)) and thesecond grating by an amount

$\phi_{d} = {\cos^{- 1}\left( \sqrt{\cos\left( {2\left( {\phi_{1} - \frac{\pi}{2}} \right)} \right)} \right)}$with respect to the first grating. In accordance with equation 1, φ₁will range from 45° for a maximum value of Γ_(x-pol) corresponding to100% reflection to 90° for a minimum value of Γ_(x-pol) corresponding to0% reflection. More typically, Γ_(x-pol) will range for −3 dB (e.g. 50%reflected power) to about −15 dB, e.g. anything less than −20 dB isessentially zero. In accordance with equation 2, φ_(d) will range from90° for maximum x-pol reflection (e.g. 135° from the incidentpolarization) to 0° for minimum x-pol reflection (e.g. 90° from theincident polarization).

Another case is where the cross-pal reflected component is nulled.

Case 2: Γ_(x-pol)=0

In this case the first grating is rotated by

$\phi_{1} = \frac{\pi}{2}$and the second grating by an amount

$\phi_{d} = {\cos^{- 1}\left( \sqrt{\frac{1 - \Gamma_{co}}{1 + \Gamma_{co}}} \right)}$with respect to the first grating. In accordance with equation 1, φ₁ isfixed for all values of co-pol reflection. In accordance with equation2φ_(d) will range from 90° for maximum x-pol reflection (e.g. 135° fromthe incident polarization) to 0° for minimum x-pol reflection (e.g. 90°from the incident polarization).

The derivation of equations (1) and (2) for the partial reflector isbased on the calculation of the scattering matrix for the structure. Weassume that the gratings that make up the structure have been designedappropriately so that they only reflect a single Floquet mode, i.e. nograting lobes are generated. This will be the case when the gratingtines are spaced less then λ/2 apart center to center. We also assumethat the gratings are designed so that the component polarized along thetines reflects perfectly (in reality there will be a small inductivephase shift) and the orthogonal component will transmit perfectly (thisis accomplished using a λ/2 depth of the tines, with a small correctionmade for fringing capacitance).

An equivalent four-port network 26 for the partial reflector is shown inFIG. 3. Port A is co-pol 18 on the input (left) side of the structure,port B is x-pol 20 on the input, port C is co-pol 21 on the output(right), and port D is x-pol 22 on the output. Elements of the structureare represented by four-port networks 28, 30 described by their Sparameters. The derivation will proceed from the center network thatrepresents the spacing s between the gratings and work its way outward.Grating 12 is represented by short circuits 32 and 34 at ports I andIII, and a λ/2 transmission line 36 connecting ports II and IV of a fourport network 28. Similarly, grating 14 is represented by short circuits38 and 40 at ports I and III, and a λ/2 transmission line 42 connectingports II and IV of a four-port network 30. This representation assumesthat the port polarizations have been defined in terms of polarizationsalong the tines for ports I and III and orthogonal to the tines forports II and IV. In reality, the gratings are rotated, and the effectsof the rotations are included using “rotation networks” 44, 46, 48 and49. Each grating has a rotation network on each side, so that wavespassing from either side have their polarizations rotated to the newbasis set for the grating. Details are given in J. J. Lynch, J. S.Colburn. “Modeling Polarization Mode Coupling in Frequency SelectiveSurfaces,” IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-52.No. 4, pp 1328-1338, April 2004.

The S par matrix for the spacing s between the gratings is S₁

${S_{t} = {\begin{pmatrix}0 & I \\I & 0\end{pmatrix}{\mathbb{e}}^{{- j}\;\theta}}},$where θ is the electric length of the spacing (90 degrees for λ/4) and Iis the identity matrix

$I = {{\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\mspace{14mu}{and}\mspace{14mu} 0} = \begin{pmatrix}0 & 0 \\0 & 0\end{pmatrix}}$is the null matrix. The use of submatrices simplifies the calculations.The rotation matrices for the right side of the left grating 12 and theleft side of the right grating 14 are given, respectively, by

${S_{u_{1}^{T}} = {{\begin{pmatrix}0 & U_{1}^{T} \\U_{1} & 0\end{pmatrix}\mspace{14mu}{and}\mspace{14mu} S_{u_{2}}} = \begin{pmatrix}0 & U_{2} \\U_{2}^{t} & 0\end{pmatrix}}},{{{where}\mspace{14mu} U_{1.2}} = {\begin{pmatrix}{\cos\left( \phi_{1.2} \right)} & {\sin\left( \phi_{1.2} \right)} \\{- {\sin\left( \phi_{1.2} \right)}} & {\cos\left( \phi_{1.2} \right)}\end{pmatrix}.}}$The scattering matrix for the spacing ‘s’ plus the two rotation matricesis given by

${S_{t^{\prime}} = {{\begin{pmatrix}0 & {U_{1}^{l}U_{2}} \\{U_{2}^{T}U_{1}} & 0\end{pmatrix}e^{{- j}\;\theta}} = {\begin{pmatrix}0 & U_{d} \\U_{d}^{l} & 0\end{pmatrix}e^{{- i}\;\theta}}}},{where}$ ${U_{d} = \begin{pmatrix}{\cos\left( \phi_{d} \right)} & {\sin\left( \phi_{d} \right)} \\{- {\sin\left( \phi_{d} \right)}} & {\cos\left( \phi_{d} \right)}\end{pmatrix}},$and φ_(d)=φ₂−φ₁ where φ₂ is the rotation of grating 14 with respect tothe incident polarization.

The next step is to apply short circuits to ports I and III of thenetwork described by S₁. The result is a 2 port network, with Sparameters given by S_(2p)=S_(a)+S_(b) ¹(Γ⁻−S_(a))⁻S_(b), where

${S_{a} = {\begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}{\cos\left( \phi_{d} \right)}e^{i\;\theta}}},{S_{b} = {\begin{pmatrix}0 & 1 \\{- 1} & 0\end{pmatrix}{\sin\left( \phi_{d} \right)}e^{{- j}\;\theta}}},$and 132 −1. After some algebraic manipulation, the resulting 2-portmatrix is found to be

${S_{2_{p}} = \begin{pmatrix}S_{2p{.11}} & S_{2p{.12}} \\S_{2p{.12}} & S_{2p{.11}}\end{pmatrix}},{{{where}\mspace{14mu} S_{2p{.11}}} = {{- \frac{{\sin^{2}\left( \phi_{d} \right)}e^{{- j}\; 2\;\theta}}{1 - {{\cos^{2}\left( \phi_{d} \right)}e^{{- j}\; 2\;\theta}}}}{and}}}$$S_{2p{.12}} = {{\cos\left( \phi_{d} \right)}{{e^{{- j}\;\theta}\left( \frac{1 - e^{{- j}\; 2\;\theta}}{1 - {{\cos^{2}\left( \phi_{d} \right)}e^{{- j}\; 2\;\theta}}} \right)}.}}$These ports must be rotated through an angle θ_(t) that represents thethickness of the tines (nominally λ/2). This inserts a factor e^(−j20)to each of the 2 port S parameters above. Next, the four port network 26is created by adding short circuits to ports I and III and using theabove 2 port between ports II and IV. The resulting scattering matrixis:

$S_{4p} = {\begin{pmatrix}{- 1} & 0 & 0 & 0 \\0 & {S_{2p{.11}}e^{{- j}\; 2\theta_{i}}} & 0 & {S_{2p{.12}}e^{{- j}\; 2\theta_{i}}} \\0 & 0 & {- 1} & 0 \\0 & {S_{2p{.12}}{\mathbb{e}}^{{- j}\; 2\theta_{i}}} & 0 & {S_{2p{.11}}{\mathbb{e}}^{{- j}\; 2\theta_{i}}}\end{pmatrix}.}$The final step is to rotate the polarizations back to the incidentpolarizations. This is accomplished by including the last 2 rotationnetworks in the computations. The resulting scattering matrix is

${S^{\prime} = \begin{pmatrix}{U_{1}S_{4p{.11}}U_{1}^{T}} & {U_{1}S_{4p{.11}}U_{2}^{T}} \\{U_{2}S_{4p{.12}}U_{1}^{T}} & {U_{2}S_{4p{.12}}U_{2}^{T}}\end{pmatrix}},$where the submatrices are given by

$\quad\begin{matrix}{{U_{1}S_{4p{.11}}U_{1}^{T}} = {\begin{pmatrix}{\cos\left( \phi_{1} \right)} & {\sin\left( \phi_{1} \right)} \\{- {\sin\left( \phi_{1} \right)}} & {\cos\left( \phi_{1} \right)}\end{pmatrix}\begin{pmatrix}{- 1} & 0 \\0 & {S_{2p{.11}}e^{{- j}\; 2\theta_{i}}}\end{pmatrix}\begin{pmatrix}{\cos\left( \phi_{1} \right)} & {- {\sin\left( \phi_{1} \right)}} \\{\sin\left( \phi_{1} \right)} & {\cos\left( \phi_{1} \right)}\end{pmatrix}}} \\{{= \begin{pmatrix}{{- {\cos^{2}\left( \phi_{1} \right)}} + {S_{2p{.11}}e^{{- j}\; 2\;\theta_{i}}{\sin^{2}\left( \phi_{1} \right)}}} & {\left( {1 + {S_{2p{.11}}e^{{- j}\; 2\theta_{i}}}} \right){\sin\left( \phi_{1} \right)}{\cos\left( \phi_{1} \right)}} \\{\left( {1 + {S_{2p{.11}}e^{{- j}\; 2\theta_{i}}}} \right){\sin\left( \phi_{1} \right)}{\cos\left( \phi_{1} \right)}} & {{- {\sin^{2}\left( \phi_{1} \right)}} + {S_{2p{.11}}e^{{- j}\; 2\;\theta_{i}}{\cos^{2}\left( \phi_{1} \right)}}}\end{pmatrix}},{{etc}.}}\end{matrix}$Since we are primarily interested in the reflections from the left(input) side of the structure, the remaining three submatrices need notbe computed.

At the center frequency of operation, we will assume the spacing is λ/4(i.e., θ=π/2) and the thickness of the tines is λ/2 (i.e., θ_(t)=π). Forthis case, the co-pol reflection is given by:

$\Gamma_{{co} - {pol}} = {{- {\cos^{2}\left( \phi_{1} \right)}} + {\frac{\sin^{2}\left( \phi_{d} \right)}{1 + {\cos^{2}\left( \phi_{d} \right)}}{\sin^{2}\left( \phi_{1} \right)}}}$and the x-pol reflection by:

$\Gamma_{x - {pol}} = {{\left( {1 + \frac{\sin^{2}\left( \phi_{d} \right)}{1 + {\cos^{2}\left( \phi_{d} \right)}}} \right){\sin\left( \phi_{1} \right)}{\cos\left( \phi_{1} \right)}} = {\frac{\sin\left( {2\phi_{1}} \right)}{1 + {\cos^{2}\left( \phi_{d} \right)}}.}}$Note that these reflection coefficients are real due to our choice ofλ/2 tine thickness and λ/4 grating separation. These expressions can bemanipulated to produce the final result given in equations (1) and (2)above. In practice the amounts of rotation will not be exactly equal tothe expressions given above due to the non-ideal nature of physicalgratings. But for gratings that are designed well and exhibit highreflection with phase reversal for polarization along the grating andhigh transmission with no additional phase delay (except possibly phasereversal), the expressions given above will be fairly accurate.

A physical explanation of the operation of the partial reflection isdescribed with reference to FIGS. 4 a-4 c for a special case in whichthe reflected x-pol component is set at a specific amount and thereflected co-pol component is nulled to zero. The principles apply toany specified amounts for both the co- and x-pol components. FIG. 4 ashows a normally-incident linearly polarized plane wave Einc 50 incidenton the first grating 12 at an angle φ₁. A portion 51 of incident wave 50is transmitted through the grating and some is reflected back. Thereflected wave can be decomposed into co-pol 52 (dashed) and x-pol 54components with respect to the incident field. Note that the reflectedcomponent is flipped (phase reversal) upon reflection. The secondgrating 14 is rotated by φ_(d) to cancel the co-pol component 52. FIG. 4b shows the transmitted wave 51 incident upon the second grating, whichis rotated with respect to the first. A portion 56 of this wave istransmitted through, and part is reflected back (with a phase reversal).This reflected wave can be decomposed into a component 58 (dashed)across the first grating and a component 60 along the first grating. Asshown in FIG. 4 c, the wave component 58 across the first grating 12 istransmitted through with a phase reversal due to the net half wavelengthdistance traveled between gratings. Wave component 58 can be decomposedinto co-polarization component 62 (bold) and a x-pol component 64 withrespect to the original incident wave. The rotation angle of the secondgrating is chosen so that the (bold) co-pol component 62 exactly cancelsthe original (dashed) co-pol component 52 reflected from the firstgrating by the incident wave. In this way the device reflects only x-polcomponent 54. The description is only approximate since it neglectsmultiple reflections between the gratings, but serves to give physicalinsight into how this device operates. The formulas given above for theco-pol and x-pol reflections are more accurate since they take multiplereflections into account.

Although the formulas are reasonably accurate for well designed gratingsand typical system applications it may be desirable to “tweak” therotation of gratings to improve accuracy. Conceivably this could be donein a few different ways. A system or operator could forgo the equationsaltogether and just rotate the gratings until the desired amount of theco- and x-pol fields was realized. Typically, one would adjust the firstgrating to approximately set the larger field, adjust the second gratingto approximately set the smaller field and than make fine adjusts.Alternately, one could use the equations to set the initial rotation ofthe gratings and than make fine adjustments. Both approaches assume that(a) the system has the capability to measure the reflected fieldcomponents, (b) the ability to rotate both gratings and (c) the time toperform the calibration. Another approach is use the equations andperform the fine adjusts off-line and store the angles for specific co-and x-pol fields in a look-up table (LUT). The LUT can than be used toprovide the angles for a fixed implementation of the partial reflectoror can be provided to a system controller as part of a variableimplementation of the partial reflector.

One method of programming the LUT is illustrated in FIG. 5. The LUT ofangle pairs φ₁, φ_(t) is programmed for a range of Γ_(x-pol), Γ_(co-pol)and a desired resolution. For example, Γ_(x-pol), Γ_(x-pol) could be (−3dB to −15 db, −3 dB to −15 dB) by increments of 0.1 dB, In anotherembodiment Γ_(x-pol), Γ_(co-pol) could be (−3 dB to −15 db, 0) byincrements of 0.1 dB, The amounts Γ_(x-pol), Γ_(co-pol) are set toinitial values (step 68) and the corresponding angles φ₁, φ_(d) arecalculated (step 70). Note, at this point the angles could be programmedinto the LUT without further adjustment. In this embodiment, thegratings are rotated to the calculated φ₁, φ_(d) (step 72) and the firstgrating is illuminated with a linearly polarized plane wave (step 74).One component, suitably the largest and in this case the x-pol field, ismeasured (step 76) and φ₁ is adjusted until the measured amount ofΓ_(x-pol) is the specified amount for the table (step 78). Similarly theother component, suitably the smaller and in this case co-pol field, ismeasured (step 80) and φ_(d) is adjusted until the measured amount ofΓ_(co-pol) is the specified amount for the table (step 82). Because theadjustment of φ_(d) may affect Γ_(x-pol) the components are remeasuredand the process is repeated until Γ_(x-pol), Γ_(co-pol) are within aspecified tolerance (step 84). At that point, φ₁, φ_(d) are stored inthe LUT for the specified values of Γ_(x-pol), Γ_(co-pol) (step 86),Γ_(x-pol), Γ_(co-pol) are incremented (step 88) and the process isrepeated until the LUT is programmed.

There are many ways to physically realize the grating structures. In oneembodiment shown in FIGS. 6 a and 6 b, a series of rectangular openings90 are cut through a plate 92 to form a series of metal tines 94 havingrectangular cross section, which together form a grating 96. The periodof the grating “a” is chosen to be ˜λ/2 to avoid spurious lobes from thegrating. The width of the tine “b” is typically chosen to be ˜λ/4.Smaller tines give better performance, but are more difficult torealize, especially at high frequencies. The thickness of the tines “d”is typically ˜λ/2 to minimize reflections of waves polarizedperpendicular to the grating. This structure is especially appealingbecause it offers minimal material loss to waves that are transmitted orreflected from it.

Another method of realizing the gratings is to utilize photolithographicprinted circuit board methods to etch a metal pattern in a planardielectric material. The circuit boards are spacing about a quarter of awavelength apart, and each of the circuit boards is about half awavelength thick. If mechanical support is needed between the boards,one could insert a spacer layer, with a thickness of about a quarter ofa wavelength in the spacer material, rather than having air between thecircuit hoards. For practical structures the grating period should beabout one quarter to three quarters of a wavelength, and the strip widthshould be between one eighth and one half of the period. Due toparasitic effects of the printed circuit gratings, the optimum rotationangles will be slightly different than those given above, but not muchdifferent for most practical structures. If variable reflectivity is notneeded, specific amounts of Γ_(x-pol), Γ_(co-pol) can be achieved with asingle dielectric sheet that has two grating patterns, each at aspecific angle relative to the incident polarization, by etching thegrating patterns on both sides of the dielectric. For this structure thedielectric should be about a quarter wavelength thick in the dielectricmaterial.

FIGS. 7 a-7 c show calculations of the co-pol and x-pol reflected fieldmagnitudes 100 a, 100 b, 100 c and 102 a, 102 b and 102 c, normalized tothe incident field magnitude, where the first grating is rotated by 60°,70° and 80° and the second grating is rotated to null the co-pol field.The reflected x-pol field is approximately constant and the co-pol fieldis less than −20 dB over an approximately 10 GHz bandwidth centered onan operating frequency of 95 GHz. The electromagnetic scattering fromthe grating was computed using Ansoft's HFSS finite element simulator,and the results were used to compute the response including therotations of the first and second gratings. The dimensions of thegrating are: a=1.27 mm, b=0.635 mm, d=1.36 mm. At 95 GHz, λ=3.16 mm. Thedimension “d” was chosen to minimize reflections for polarizationsorthogonal to the bars. It is slightly less than λ/2 due to the effectsof fringing capacitance at the edges of the bars.

As shown in FIG. 8, a mechanically tunable reflector 110 includes a pairof inner grating plates 112 and 114, each with a grating formed therein.The plates are spaced approximately_(—)¼ apart and held in place byouter anchor plates 116 and 118 and screws (not shown) through outerflanges 119. Ball hearing races (not shown) between the inner gratingplates and the outer anchor plates allow the inner grating plates torotate freely. A tuning mechanism 120 such as a pair of stepper motorsindependently rotates each grating to a desired angle. In thisembodiment, the relationship between (φ₁, φ_(d)) and (Γ_(x-pol),Γ_(co-pol)) is stored in a LUT 122 in memory 124. The system or anoperator specifics Γ_(x-pol), Γ_(co-pol) and the LUT outputs thecorresponding (φ₁, φ_(d)) to tuning mechanism 120. Depending on thegranularity of the LUT and the system requirements, the closest pair canbe used or a simple interpolation can be performed to improve theprecision of the angles.

As shown in FIGS. 9 and 10, a variable cross-coupling partial reflector200 can be incorporated into a quasi-optical electromagnetic arraystructure 202 to generate high power either as a source or as anamplifier at millimeter wave frequencies depending on the amount ofarray coupling. The variable cross-coupling partial reflector canprovide the desired reflected x-pol field to provide amplification oroscillation while nulling the co-pol field to improve power efficiencyof the source.

The structure utilizes amplification devices 204 with cross input/outputpolarizations arranged in an array 206. The amplification deviceincludes an input antenna 208 polarized in the X direction, an amplifier210, and an output antenna 212 polarized in the Y direction. The arrayof amplification devices are disposed on a heatsink layer 214 with awaveguide 216 coupled to the array for coupling in the input wave. Thewaveguide 216 is needed only for the amplifier or amplifier/oscillatorconfigurations but not for an oscillator only configuration. Partialreflector 200 is rotationally disposed above the array so that its firstand second gratings 218 and 220 may rotate independently.

By configuring the partial reflector 200 to reflect 100% of theco-polarized energy in the X direction and to transmit 100% of thecross-polarized energy in X direction, the structure operates as a highpower amplifier. The energy from an opening of the waveguide 216 isreflected off of the partial reflector, absorbed by the input antennas208, amplified by amplifier 210 and reradiated by the output antennas212 in the cross polarization Y direction, which allows it to passmostly unaffected through the partial reflector. To achieve this bothgratings are suitably aligned parallel with the polarization of theinput antenna in the X direction.

By configuring the partial reflector 200 to reflect a specified amountof cross-polarized energy in the X direction, the structure operates asan oscillator. Some of the output energy is converted intocross-polarized modes, thus coupling together the amplifier inputs andoutputs. If the cross-polarized coupling is increased beyond a certainthreshold, the amplification is high enough to overcome losses in thesystem and the round trip phase is close to zero, the feedback willcause the amplification devices to oscillate. Configuring the partialreflector to null the co-polarized energy in the Y direction willimprove the power efficiency of the structure.

While several illustrative embodiments of the invention have been shownand described, numerous variations and alternate embodiments will occurto those skilled in the art. Such variations and alternate embodimentsare contemplated, and can be made without departing from the spirit andscope of the invention as defined in the appended claims.

1. A cross-coupling partial reflector, comprising: a first frequencyselective surface (FSS) rotated by a first angle with respect to thepolarization of an incident plane wave, and a second FSS spaced behindthe first FSS and rotated by a second angle with respect to the firstFSS, said first and second FSSs substantially reflective to polarizedwaves of one polarization and substantially transmissive to theorthogonally polarized waves, said first and second FSSs reflecting theincident plane wave so that the magnitude of a net reflection hasapproximately a specified amount of a cross-polarized field of the planewave and approximately a specified amount of a co-polarized field of theplane wave and transmitting the remaining energy in co-polarized andcross-polarized fields.
 2. The partial reflector of claim 1, whereinsaid first and second FSSs are gratings.
 3. The partial reflector ofclaim 1, wherein the spacing between the first and second FSSs is not ahalf-wavelength or a multiple thereof of the incident plane wave.
 4. Thepartial reflector of claim 1, wherein the spacing is approximately anodd multiple of a quarter-wavelength of the incident plane wave.
 5. Thepartial reflector of claim 4, wherein the spacing is approximately onequarter-wavelength of the incident plane wave.
 6. The partial reflectorof claim 1, wherein the first and second FSSs are rotated so that theamount of one of the reflected co-polarized or cross-polarized fieldslies in a non-zero range normalized to the incident plane wave and theother reflected field is approximately nulled over a predeterminedbandwidth.
 7. The partial reflector of claim 1, further comprising: atuning mechanism that rotates the first FSS with respect to thepolarization of an incident plane wave to said first and rotates thesecond FSS with respect to the first FSS to said second angle to providethe specified amounts of the cross-polarized and co-polarized fields. 8.The partial reflector of claim 7, further comprising: memory for storingpairs of said first and second angles for pairs of specified amounts ofthe reflected cross-polarized and co-polarized fields.
 9. The partialreflector of claim 1, wherein said reflected cross-polarized andco-polarized fields are either in-phase or 180° out of phase.
 10. Thepartial reflector of claim 1, wherein φ₁ and φ_(d) are said first andsecond angles and Γ_(x-pol) and Γ_(co-pol) are the specified amounts ofthe reflected, magnitudes of cross-polarized and co-polarized fieldsrespectively, wherein to a reasonable approximation,${\phi_{1} = {\cot^{- 1}\left( \frac{\Gamma_{x - {pol}}}{1 + \Gamma_{{co} - {pol}}} \right)}},{and}$$\phi_{d} = {{\cos^{- 1}\left( \sqrt{\frac{{\cos\left( {2\left( {\phi_{1} - \frac{\pi}{2}} \right)} \right)} - \Gamma_{{co} - {pol}}}{1 + \Gamma_{{co} - {pol}}}} \right)}.}$11. The partial reflector of claim 1, wherein the achievable specifiedamounts of reflected Γ_(x-pol) and Γ_(co-pol) lie inside an outer circleof |Γ_(co-pol)|²+|Γ_(x-pol)|²=1 and outside an inner circle of|Γ_(co-pol)=0.5|²+|Γ_(x-pol)|²=0.25.
 12. The cross-coupling partialreflector of claim 1, wherein the remaining energy in the co-polarizedand cross-polarized fields is transmitted through the cross-couplingpartial reflector in the same direction as the incident plane wave. 13.The cross-coupling partial reflector of claim 1, wherein the specifiedamounts of the cross-polarized and co-polarized fields that arereflected are different amounts.
 14. A variable cross-coupling partialreflector for reflecting a linearly-polarized plane wave normallyincident on the reflector so that the magnitude of the net reflectionhas a specified amount Γ_(x-pol) of a cross-polarized field and aspecified amount Γ_(co-pol) of a co-polarized field, comprising: a firstgrating; a second grating spaced a distance behind the first grating,said first and second gratings substantially reflective to polarizedwaves of one polarization and substantially transmissive to theorthogonally polarized waves; and a tuning mechanism that rotates thefirst grating by an angle φ₁ with respect to the polarization a thelinearly-polarized plane wave normally incident on the reflector androtates the second grating by an angle φ_(d) with respect to the firstgrating, wherein to a reasonable approximation${\phi_{1} = {\cot^{- 1}\left( \frac{\Gamma_{x - {pol}}}{1 + \Gamma_{{co} - {pol}}} \right)}},{and}$$\phi_{d} = {\cos^{- 1}\left( \sqrt{\frac{{\cos\left( {2\left( {\phi_{1} - \frac{\pi}{2}} \right)} \right)} - \Gamma_{{co} - {pol}}}{1 + \Gamma_{{co} - {pol}}}} \right)}$said first and second gratings reflecting the incident plane wave sothat the magnitude of a net reflection has approximately the specifiedamount Γ_(x-pol) of a cross-polarized field of the plane wave andapproximately the specified amount Γ_(co-pol) of a co-polarized field ofthe plane wave and transmitting the remaining energy in co-polarized andcross-polarized fields.
 15. The partial reflector of claim 14, furthercomprising: a look-up table storing angle pairs (φ₁, φ_(d)) pairs forspecified (Γ_(x-pol), Γ_(co-pol)) pairs.
 16. The partial reflector ofclaim 14, wherein Γ_(co-pol) is approximately
 0. 17. The partialreflector of claim 14, wherein said reflected cross-polarized andco-polarized fields are either in-phase or 180° out of phase.
 18. Thepartial reflector of claim 14, wherein the achievable specific amountsof reflected Γ_(x-pol) and Γ_(co-pol) lie inside an outer circle of|Γ_(co-pol)|²+|Γ_(x-pol)|²=1 and outside an inner circle of|Γ_(co-pol)+0.5|²+|Γ_(x-pol)|²=0.25.
 19. A method of controllingreflected power from an incident plane wave, comprising: providing afirst frequency selective surface (FSS) in the path of a polarized planewave; providing a second FSS behind the first FSS in said path, saidfirst and second FSSs substantially reflective to polarized waves of onepolarization and substantially transmissive to the orthogonallypolarized waves; rotating said first FSS by a first angle with respectto the polarization of the incident plane wave and rotating the secondFSS by a second angle with respect to the first FSS; reflecting theincident polarized plane wave off of the first and second FSSs so thatthe magnitude of a net reflection has approximately a specified amountof a cross-polarized field of the plane wave and approximately aspecified amount of a co-polarized field of the plane wave; andtransmitting the remaining energy through the first and second FSSs inco-polarized and cross-polarized fields.
 20. The method of claim 19,wherein the said first and second FSS are spaced apart by aquarter-wavelength of the incident plane wave or an odd multiplethereof.
 21. The method of claim 19, wherein the first and second FSSsare rotated so that the amount of one of the reflected co-polarized orcross-polarized fields lies in a non-zero range normalized to theincident plane wave and the other reflected field is approximatelynulled over a predetermined bandwidth.
 22. The method of claim 19,further comprising: storing pairs of said first and second angles forpairs of specific amounts of the reflected cross-polarized andco-polarized fields in memory; and reading a pair of said first andsecond angles from memory for the specified amounts of reflectedcross-polarized and co-polarized fields.
 23. The method of claim 19,wherein φ₁ and φ_(d) are said first and second angles and Γ_(x-pol) andΓ_(co-pol) are the specific amounts of the cross-polarized andco-polarized fields respectively, wherein said first and second FSS arerotated to φ₁ and φ_(d) which to a reasonable approximation are givenby:${\phi_{1} = {\cot^{- 1}\left( \frac{\Gamma_{x - {pol}}}{1 + \Gamma_{{co} - {pol}}} \right)}},{and}$$\phi_{d} = {{\cos^{- 1}\left( \sqrt{\frac{{\cos\left( {2\left( {\phi_{1} - \frac{\pi}{2}} \right)} \right)} - \Gamma_{{co} - {pol}}}{1 + \Gamma_{{co} - {pol}}}} \right)}.}$24. The method of claim 23, further comprising: measuring the actualreflected fields Γ_(x-pol) and Γ_(co-pol); and adjusting the rotation ofsaid first and second FSSs until the measured Γ_(x-pol) and Γ_(co-pol)are within an acceptable tolerance of the specific amounts of thereflected co-polarized or cross-polarized fields.
 25. A quasi-opticalelectromagnetic array structure, comprising: cross-polarized input andoutput antennas; an amplifier array that amplifies energy absorbed bythe input antenna and reradiates the amplified energy from the outputantenna; and a partial reflector including first and second frequencyselective surfaces (FSSs), said first and second FSSs substantiallyreflective to polarized waves of one polarization and substantiallytransmissive to the orthogonally polarized waves, said first FSS rotatedat a first with respect to the polarization of the input antenna andsaid second FSS rotated at a second angle with respect to the first FSSso that a net reflection of energy reradiated from the output antennaand incident on the cross-coupling reflector has approximately specifiedamount of a cross-polarized field and approximately a specified amountof a co-polarized field with respect to the polarization of the inputantenna, said remaining energy transmitted through the partial reflectorin co-polarized and cross-polarized fields.
 26. The quasi-opticalelectromagnetic array structure of claim 25, wherein said structureoperates as an oscillator by setting said first and second angles so asto induce oscillations and synchronize said amplifier array to producecoherent power.
 27. The quasi-optical electromagnetic array structure ofclaim 26, wherein said first and second angles are set to approximatelynull the co-polarized field.
 28. A quasi-optical electromagnetic arraystructure, comprising: a plurality of active amplification devicesarranged in an array, wherein an input of each active amplificationdevice is cross-polarized with respect to an output of each activeamplification device; and a partial reflector disposed in a spacedrelation with the plurality of active amplification devices so as tocouple cross polarized input and output of each active amplificationdevice, wherein said partial reflector includes: a first frequencyselective surface (FSS) rotated by a first angle with respect to theinput, and a second FSS spaced behind the first FSS and rotated by asecond angle with respect to the first FSS, said first and second FSSssubstantially reflective to polarized waves of one polarization andsubstantially transmissive to the orthogonally polarized waves, wherebya net reflection of energy radiated from the output and incident on thepartial reflector has approximately a specified amount of across-polarized field and approximately a specified amount of aco-polarized field with respect to the polarization of the input, saidremaining energy transmitted through the partial reflector inco-polarized and cross-polarized fields.
 29. The quasi-opticalelectromagnetic array structure of claim 28, wherein said structureoperates as an amplifier by setting said first and second angles so asto cause an incoming energy to be absorbed by the input of each activeamplification device, amplified and reradiated in the crossedpolarization from the output of each active amplification device. 30.The quasi-optical electromagnetic array structure of claim 28, whereinenergy waves propagate through an input waveguide coupled to the activeamplification devices and reflect off of the first and second FSSs intothe inputs of each active amplification device, and after amplificationare at least partially reradiated in a cross polarization from theoutput of each active amplification device through the partialreflector.
 31. The quasi-optical electromagnetic array structure ofclaim 28, wherein said structure operates as an oscillator by settingsaid first and second angles so as to induce oscillations andsynchronize said plurality of active devices to produce coherent power.32. The quasi-optical electromagnetic array structure of claim 31,wherein said first and second angles are set to approximately null theco-polarization.
 33. The quasi-optical electromagnetic array structureof claim 31, wherein energy waves reflect off of the first and secondFSSs into the inputs of each active amplification device and afteramplification are at least partially reradiated in a cross polarizationfrom the output of each active amplification device through the partialreflector.